The components are mathematical/theoretical constructs....the components would NOT be the 2 year and the 30 year if you were to use PCA in your example. PCA in a problem with only 2 independent variables would be inappropriate. I forget the details, so some of my statements may be off slightly, but if I remember correctly, PCA is appropriate for high dimensional problems. It is a dimension reduction technique used in multivariate statistics. The PCA approach identifies eigenvalues/eigenvectors that "explain" the behavior of the data. Eigenvalues/vectors are, by definition, perpendicular, or in other words, uncorrelated, i.e., their dot products are 0. Say you have 10 eigenvalues....the first 4 of them might explain 95% of the behavior in the data, so you could effectively utilize the 4 principal components associated with the 4 eigenvalues rather than using all 10 since last 6 appear unimportant as they explain only 5% of the behavior. So, you will have reduced the dimensionality down from 10 to 4.
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